IPMAT Set Theory Questions 2027: 25+ Practice Questions with Solutions

Are you preparing for a management exam and searching for IPMAT Set Theory questions to boost your Quantitative Ability skills? Set Theory is an important topic, and it becomes much easier once you know the basic formulas and how to use them.

IPMAT 2027 Set Theory questions often cover topics like union, intersection, subsets, complements, Venn diagrams, cardinality, and inclusion-exclusion.

Some are straightforward, while others are word problems about students, subjects, sports, languages, or preferences.

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Here we cover key concepts, formulas, and Set Theory questions for IPMAT, along with solutions. You’ll also find practice questions at different difficulty levels to help you get ready for the quantitative section for the IPMAT 2027.

If you want an IPMAT Set Theory Questions PDF, just save this page as a PDF and use it for revision.

What Are Set Theory Questions in IPMAT 2027?

A set is a well-defined collection of objects or elements. For example: A = {2, 4, 6, 8, 10}

Here, A is a set containing five elements. In aptitude questions, sets are often used to represent different groups. For example, we can have:

• A = students who like Mathematics
• B = students who like English
• C = students who like Reasoning

The question may then ask how many students like both subjects, at least one subject, only one subject, or none.

This is where Venn diagrams and set formulas become useful.

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Important Set Theory Concepts for IPMAT 2027

Before you start solving IPMAT Set Theory questions, make sure you understand the basic concepts and operations. The table below gives you a quick review of the key ideas.

Set Theory Concept	Meaning	Symbol
Union of Sets	Contains all elements that belong to either set or both sets. Common elements are written only once.	A ∪ B
Intersection of Sets	Contains elements that are common to both sets.	A ∩ B
Difference of Sets	Contains elements that belong to one set but not the other.	A − B
Difference of Sets (B − A)	Contains elements that belong to B but not to A.	B − A
Complement of a Set	Contains elements of the universal set that are not present in the given set.	A′ or Aᶜ
Cardinality of a Set	Represents the total number of elements in a set.	n(A)

Important Set Theory Formulas for IPMAT 2027

These formulas are especially helpful for solving Set Theory questions in IPMAT. Knowing them will help you answer Venn diagram and word problems faster.

SET Theory Formulas for Two Sets

Formula / Requirement	Formula
Union of two sets	n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
Intersection of two sets	n(A ∩ B) = n(A) + n(B) − n(A ∪ B)
Elements in A only	n(A − B) = n(A) − n(A ∩ B)
Elements in B only	n(B − A) = n(B) − n(A ∩ B)
Elements in neither A nor B	n(U) − n(A ∪ B)
Elements in exactly one of A and B	n(A) + n(B) − 2n(A ∩ B)

IPMAT SET Theory Questions to Practice in 2027

Q1. In a group of 150 students, 52 like tea, 48 like juice and 62 like coffee. If each student likes at least one drink, the maximum number who like more than one drink is ___ [IPMAT Indore 2024]
(a) 10

(b) 12

(c) 14

(d) 16

Hint: n(T)+n(J)+n(C) − n(union) = y + 2z (y = exactly two, z = exactly three). Maximize (y+z) by setting z = 0.

Answer: (b) 12 — 162 − 150 = 12 = (y+z)+z, maximized when z=0, y=12.

Q2. In a survey of 500 people: 250 owned a 4-wheeler but not a 2-wheeler, 100 owned a 2-wheeler but not a 4-wheeler, 100 owned neither. Number who owned both? [IPMAT Indore 2024]
(a) 75

(b) 60

(c) 50

(d) 100

Hint: n(FW∪TW) = 500 − 100 (neither). Then use the union formula to isolate the intersection.

Answer: (c) 50 — 400 = 250+100 − n(FW∩TW) → 50.

Q3. In a group of 120 students, 80 are Science and 40 are Commerce. 70 support Mumbai Indians (the rest support CSK). Number of Science students supporting MI? [IPMAT Indore 2023]
(a) Exactly 20

(b) Between 15 and 25

(c) Between 20 and 25

(d) 30 or more

Hint: Commerce can supply at most 40 MI supporters — find the minimum Science must contribute.

Answer: (d) 30 or more.

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Q4. In a survey of 100 students: English only-18, English but not Hindi-23, English∩German-8, English-26, German-48, German∩Hindi-8, no language-24. Which statements are true — A) Hindi=18, B) English∩Hindi=3, C) English∩Hindi∩German=3? [JIPMAT 2023]

(a) A and B only

b) A and C only

(c) B and C only

 (d) A, B and C

Hint: Build a 3-set Venn diagram step by step from the given values.

Answer: (d) A, B and C — all three check out.

Q5. Let P(X) be the power set of X. If A is the null set, the number of elements in P(P(P(P(A)))) is ___ [IPMAT Indore 2022]
(a) 4

(b) 8

(c) 16

(d) 32

Hint: A set with n elements has a power set with 2ⁿ elements. Apply this four times, starting from 0.

Answer: (c) 16 — 0→1→2→4→16.

Q6. Let A = {1,2,3}, B = {a,b}. Assuming all relations from A to B are equally likely, probability that a relation is also a function? [IPMAT Indore 2022]
(a) 1/2 (

b) 3²/2⁶

(c) 1/8

(d) 1

Hint: Total relations = 2^(mn); total functions A→B = n^m.

Answer: (c) 1/8

Q7. A × B has four elements, two of which are (1,4) and (4,1). Then: [IPMAT Indore 2022]
(a) ∅ ∈ A × B

(b) A × B = B × A

(c) None of these

(d) A × B ≠ B × A

Hint: Both ordered pairs existing force 1 and 4 into both sets.

Answer: (b) A × B = B × A — A = B = {1,4}.

Q8. 60% passed Physics, 68% passed Maths. At least what % passed both? [IPMAT Indore 2021]
(a) 20%

(b) 28%

(c) 32%

(d) 40%

Hint: To minimize the intersection, maximize the union (cap at 100%).

Answer: (b) 28% — 68+60−100 = 28.

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Q9. 50% of a city speaks exactly one of Hindi/English/Tamil; 40% speak at least two; "none" = 2× "all three". 52% speak Hindi; 25% speak exactly one of English/Tamil. % who speak Hindi and exactly one more language? 
(a) 22%

(b) 25%

(c) 30%

(d) 38%

Hint: Solve the Venn regions step by step; "exactly one" + "at least two" = 90% gives the "none" group.

Answer: (a) 22%.

Q10. Out of 80 students, 50 passed Maths, 30 Physics, 40 Chemistry. At most 20 passed any pair. Max who passed all three? [IPMAT Indore 2020]
(a) 10

(b) 15

(c) 20

(d) 25

Hint: Rearrange the 3-set inclusion-exclusion formula to isolate the triple intersection.

Answer: (c) 20 — 80+60−120 = 20.

Q11. P = {2,...,25}. Q(k) = {x∈P : x>k, k divides x}. Elements in P − ∪Q(k)? [IPMAT Indore 2019]
(a) 7

(b) 8

(c) 9

(d) 10

Hint: The union covers every composite number — think about what's left.

Answer: (c) 9 — the primes {2,3,5,7,11,13,17,19,23}.

Q12. 70% like cricket, 50% like football. If x% like both: [IPMAT Indore 2019]

(a) 20 ≤ x ≤ 50

(b) x ≤ 2

(c) x ≥ 50

(d) 10 ≤ x ≤ 70

Hint: Minimum overlap when union = 100%; maximum overlap when the smaller group is fully contained in the larger.

Answer: (a) 20 ≤ x ≤ 50.

Q13. Class of 65: 40 cricket, 25 football, 20 hockey; 10 cricket&football, 8 football&hockey, 5 all three. Cricket & hockey overlap? [IPMAT Indore 2019]
(a) 7

(b) 8

(c) 10

(d) 12

Hint: Plug values into the 3-set formula and solve for the unknown.

Answer: (a) 7.

Q14. A, B finite sets; n(A−B), n(A∩B), n(B−A) in AP. If n(A∪B) = 18, n(A)+n(B) is: 
(a) 30

(b) 27

(c) 36

(d) 24

Hint: AP terms sum to 18 → middle term (A∩B) = 6; solve for y using 3y=18.

Answer: (d) 24.

Q15. (Bonus — not from the original PDF, added for practice)
In a survey of 200 students, 90 study Physics, 80 Chemistry, 70 Maths. 30 Physics&Chemistry, 25 Chemistry&Maths, 20 Physics&Maths, 10 all three. How many study none?
(a) 5

(b) 15

(c) 25

(d) 35

Hint: Find n(P∪C∪M) via inclusion-exclusion, subtract from 200.

Answer: (c) 25 — union = 175, none = 200−175 = 25.

How to Identify What a Set Theory Question Is Asking?

A common way to make mistakes is by misunderstanding keywords. Here are some common phrases you should know.

Wording in Question	What It Usually Means
At least one	Union
Both A and B	Intersection
A only	A − B
B only	B − A
Neither A nor B	Outside A ∪ B
Exactly one	A only + B only
All three	A ∩ B ∩ C
At least two	Belonging to two or more sets
None	Outside all relevant sets

Example

If a question says:

“How many students like Mathematics but not English?”

You need:

Mathematics only = n(M) − n(M ∩ E)

This does not just mean the total number of Mathematics students.

Common Mistakes in IPMAT Set Theory Questions 2027

Here are some of the most common mistakes that students usually make while preparing for SET theory questions in 2027:

1. Confusing “At Least One” With “Exactly One”

At least one includes people who belong to both sets.

Exactly one excludes people who belong to both.

It’s very important to understand this difference.

2. Forgetting the Universal Set

When finding a complement, you must know what the universal set is.

If you don’t know what U is, you can’t find Aᶜ correctly.

3. Doing Everything Mentally

Even if the calculations seem easy, drawing a small Venn diagram can help you avoid mistakes.

This is especially helpful when a question has several overlapping groups.

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How to Prepare for Set Theory for IPMAT 2027?

If Set Theory is a weak area for you, don’t try to learn everything at once.

A simple preparation strategy works better.

Step 1: Understand the Basic Definitions

It is very important to know the basics of the topic while preparing for the IPMAT exam. You can start with

Start with:

• Set
• Element
• Subset
• Universal set
• Union
• Intersection
• Difference
• Complement

Make sure you understand what each term means before moving to difficult questions.

Step 2: Memorise the Core Formulas

Every question uses a formula, so remember the basics before moving on to set theory formulas. To help you, download the complete list of Maths formulas for IPMAT 2027.

Step 3: Practise Venn Diagrams

Start practising the questions based on Venn Diagrams. Try to solve questions involving:

• Two groups
• Three groups
• Only one group
• Both groups
• Neither group

Drawing the diagram initially may take some time, but with practice you will become faster.

Step 4: Solve Different Types of Questions

There are various types of questions that will help boost your practice. Don’t solve 30 questions that all use the same formula.

Instead, mix:

• Direct questions
• Venn diagram questions
• Subset questions
• Word problems
• Two-set questions
• Three-set questions

This will improve your ability to identify the right approach.

Step 5: Practise Under Time Pressure

Once your accuracy is good, introduce a time limit. The objective should be:

Accuracy first → speed second.

If you try to answer questions quickly before you understand the concept, you’ll keep making the same mistakes.

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How Many Set Theory Questions Should You Practise for IPMAT?

There isn’t a set number of questions that guarantees mastery. Instead of focusing only on quantity, focus on variety.

A useful practice progression is:

Stage 1: Start with 10–15 basic questions

Stage 2: Next, move to 15–20 moderate questions

Stage 3: Next, select 10–15 mixed questions

Stage 4: Finally, timed practice questions

After every practice session, note down the questions you got wrong and identify the reason.

For example:

• Formula error
• Calculation error
• Misread the question
• Confused “only” and “both”
• Forgot the intersection
• Took too much time

This error log can become extremely useful during revision.

Conclusion

Set Theory can become a scoring area in your IPMAT Quantitative Ability preparation if you understand the concepts instead of simply memorising formulas.

Begin with union, intersection, difference, complements, and subsets. Then try Venn diagram problems and three-set questions. Watch out for words like “only,” “both,” “at least one,” “exactly one,” and “neither.”

The best way to learn is to review the concepts and practise regularly. If you get a question wrong, figure out why and add it to your revision list.

With enough practice, you’ll quickly spot the structure of most IPMAT Set Theory questions and pick the right formula without wasting time.

Keep this guide nearby for revision, practise the questions often, and work on getting both faster and more accurate.

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